Fabrication of Salvinia-inspired surfaces for hydrodynamic drag reduction by capillary-force-induced clustering

For decades, bioinspired functional materials have been attracting the interest of many researchers for their remarkable characteristics. In particular, some plant leaves are well known for their inherent superhydrophobic nature. Salvinia molesta, a free-floating aquatic fern, has egg-beater-shaped hierarchical trichomes on its surface of leaves. Due to the unique structure and complex wettability of the hairs, this plant has the ability to maintain a stable thick air layer upon the structure when it is submerged underwater. Often referred to as the “Salvinia Effect,” this property is expected to be suitable for use in hydrodynamic drag reduction. However, due to the complex shape of the trichome, currently applied fabrication methods are using a three-dimensional printing system, which is not applicable to mass production because of its severely limited productivity. In this work, artificial Salvinia leaf inspired by S. molesta was fabricated using a conventional soft lithography method assisted with capillary-force-induced clustering of micropillar array. The fabrication method suggested in this work proposes a promising strategy for the manufacturing of Salvinia-inspired hydrodynamic drag reduction surfaces.

of the clustered hairs were not considered in previous research, and no studies have been conducted to evaluate the HDR performance of fabricated Salvinia-inspired surfaces.
Meanwhile, capillary-force-induced clustering (CFIC), or capillaryforce-induced collapse, is the cause of major defects due to the collapse of the structure with a relatively high aspect ratio in various MEMS fabrication processes by the surface tension of the liquid, such as developer solution 26,27 . The aspect ratio of the structure, the geometric period of the pattern, the elastic modulus of the material, and the surface tension of the liquid are involved in the CFIC behavior 28,29 . By appropriately adjusting these parameters, similar to self-assembly, artificially inducing a uniform CFIC of microstructure to fabricate functional surfaces is possible [30][31][32] .
In the present study, regularly clustered arrays of pillars, such as S. molesta, were fabricated by intentionally inducing the CFIC phenomenon. Periodically repetitive pattern structure designed to induce uniform CFIC could be easily replicated through conventional soft lithography using polydimethylsiloxane (PDMS). Salvinia-like overall superhydrophobicity and local hydrophilicity at the clustered tips could be achieved through simple solution coating processes. In addition, the applicability of the fabricated Salvinia-inspired surface to the HDR functional surface was evaluated via the effective slip length measurement experiment using a rotational rheometer.

Results and discussion
Design of the master mold The dimension of the pillar structure should be carefully designed to achieve sufficient structural stability while still being deformable to the capillary interaction force to induce uniform clustering of the micropillar array 28 . In addition, dimensions, such as the height of the pillar and the distance with neighboring pillars, should be designed for the clustering angle at the tips of pillars to be as high as possible.
Here, PDMS was chosen as the replicating material to prepare the micropillar array template due to its well-established properties, including low modulus 33,34 . Polyvinyl alcohol (PVA) solution was used as a liquid to induce the capillary interaction force. After the PVA solution was dried, a thin PVA membrane could temporarily hold the clustered PDMS pillar tips together 35,36 . The PVA solution was prepared with a low concentration for high surface tension, which could induce efficient tip clustering 37 .
To induce the intended uniform clustering of micropillars, disruption of the micropillar arrangement due to structural collapse should be avoided. Firstly, the micropillar should be stable against selfcollapse due to the gravity and adhesion between the ground and adjacent pillars. For stability against gravity-induced buckling, the critical aspect ratio of the structure against buckling ð h d Þ cb is given as where h and d are the height and diameter of the pillar, respectively; E is the elastic modulus, ρ is the density of the material; and g is the gravitational acceleration 38 . For stability against ground collapse and lateral collapse, the critical aspect ratio against ground collapse ð h d Þ cg and lateral collapse ð h d Þ cl are respectively given as where w is the separation between adjacent pillars; and υ and γ SV are the Poisson's ratio and surface energy of the material, respectively 39,40 .
The critical conditions at which a collapse type makes the pillars more vulnerable than the others could be obtained as follows: For PDMS, by substituting the material properties into the above equations, the critical conditions for collapse vulnerability could be simplified as follows: For three-subpillar design as shown in Fig. 2a, b, the separation between adjacent pillars w is equal to ffiffiffi 3 p r c , where r c is the center-tocenter radius 41 .
As shown in Eqs. (6) and (7), the material properties, the diameter, and the lateral separation of the pillars determine the type of collapse that the pillars are most vulnerable to. Equation (6) shows the critical condition in which micropillars become more susceptible to either type of collapse, buckling or lateral collapse. Equation (7) represents the critical condition in which micropillars become more susceptible to either lateral collapse or ground collapse. The diagram depicting these equations and regions of the most vulnerable collapse type is shown in Fig. 2e, and Supplementary Fig. 1. Making the design point lies in the lateral collapse region so that only the stability against lateral collapse should be considered is desirable to make micropillars sufficiently stable against any type of collapse but vulnerable to capillary interaction force.
Structural deflection of the micropillar against capillary interaction force should be considered to ensure regular clustering of the pillar arrays 28,42 . The capillary interaction force at the tip of the pillar should be higher than the restoring force of the pillar in the range up to the maximum deflection, that is, the distance from the original point to the intended clustering point, r c . The capillary interaction force between partially immersed identical pillars is given as where γ LV is the interfacial surface energy of the liquid, d t is the diameter of the micropillar tip, and θ r is the receding contact angle 27 . In the case of the three-pillar design shown in Fig. 2a, b, the capillary interaction force F cc exerting on a tip of a subpillar to the center of the lower pillar should be at least higher than the restoring force of the pillar, in the region of 0 < δ < r c 28,43,44 , where d b is the diameter of the micropillar base. Typical cases of capillary force and elastic restoring force according to the deflection are shown in Supplementary Fig. 2.
The critical condition for F cc to be higher than F E could be acquired from a discriminant The critical condition plot is shown in Fig. 2f, and Supplementary Fig. 3.
In addition, to maximize the water repellency of the surface, the clustered pillar array should have gentle curvature, ideally making a horizontal angle to the water at the clustered tips. With the additional contact area per height difference due to the gently bent upper pillars, the energy required for the water to penetrate into the clustered region increases 19 . The angle at the clustered pillar tips could be described implicitly as where φ 0 is the angle at the deflected tip 45 . The higher clustering angle φ 0 , the lower the angle between the clustered pillars and the  water surface. The clustering angle as a function of the pillar height and center-to-center radius is depicted in Fig. 2f.
To sum up, to effectively mimic the "Salvinia Effect" by utilizing CFIC, the pillar should be sufficiently stable to prevent self-collapse but sufficiently flexible to be clustered together to the capillary interaction force, making a minimum angle with the water-air interface by increased clustering angle. An appropriate design point satisfying all these conditions should be slightly above the clustering critical condition plot shown in Fig. 2f.
With desirable design parameters chosen by considering the above conditions, hexagonal periodic arrays of hierarchical micropillar were designed, as shown in Fig. 2g, h. The pillars were arrayed with periods of 350 μm for lower pillars and center-to-center radius of 100 μm for upper pillars. The lower pillars have a low aspect ratio to grant structural stability while granting more height to upper pillars. The upper pillars have a relatively high aspect ratio to be easily bent, clustered, and then form a similar structure to the hairs of S. molesta. The lower and upper pillars were tapered with angles of 5.8 and 3 degrees, respectively, for easier release in the replication step and higher curvature at the tips of the upper pillars when clustered. The upper pillars have height of 220 μm, base diameter of 40 μm, and tip diameter of 17 μm. The distance among three upper pillars on a lower pillar was slightly closer than that with the others for the capillary force to be directed towards the center of the lower pillar. The hierarchical pillar structures were arrayed hexagonally, as shown in Fig. 2g, h, to induce symmetric, regular capillary interaction force on each pillar. Unlike living S. molesta, which has four upper hairs divided from a stem, three upper pillars were assigned for each lower pillar. Regularly arranging the pattern was easier with three upper pillars rather than four. The hierarchical pillar pattern was designed without any overhang or complex part to make it easy to replicate the structure with the conventional lithographic replication process.

Fabrication of the Salvinia-inspired surfaces by capillary-forceinduced clustering
From the design, a positive master mold was fabricated using 2PP 3D printing system. The master mold went through surface passivation process for easier release. Samples for the test were prepared through two successive soft lithography steps. First, the PDMS precursor was cast on the master mold, desiccated, and cured in 70°C oven for 2 h before being demolded to prepare a negative type mold. The negative type PDMS mold underwent additional overcuring in 150°C oven for 2 h for defect-free self-replication. From the negative type PDMS stamp mold, the positive PDMS replica was prepared by following the same typical soft lithographic process. PVA solution was cast on the as-prepared positive PDMS template and then evaporated in 70°C convection oven for 2 h. During the evaporation of the PVA solution, the tips of the three upper pillars were clustered together at the center due to the capillary interaction force of the solution, as shown in Fig. 3. The three upper pillars clustered together were temporarily fixed together due to the thin PVA film formed on their hemispherical tips. Given that the PVA film holding the clustered pillars together is fragile, the PDMS precursor was additionally inked and cured at the clustered tips to permanently fix the clustered tips together. Then, the sample was coated with a hydrophobic wax solution to make the entire surface superhydrophobic. The clustered tips were additionally coated with polydopamine (PDA) by making the surface partially submerged by the PDA solution to grant local hydrophilicity. In this procedure, only the clustered tips made direct contact with the PDA solution due to the superhydrophobicity of the surface. Schematics and microscopic images of the entire fabrication process are shown in Fig. 4, and Supplementary Figs. 4, 5.

Characterization of the fabricated surfaces
Scanning electron microscopic images of the fabricated sample are shown in Fig. 5. The clustering angle of micropillars after the CFIC was measured to be 54.3 ± 1.5°, which is in a good agreement with the theoretical expectation from Eq. (12). The hydrophilic tip part is visually noticeable, while the other parts are covered with hydrophobic nano wax crystals. As shown in Supplementary Fig. 6, the fabricated sample surface shows superhydrophobicity with high water contact angle of 174.9°± 3.2°. Due to the PDA coated hydrophilic tips, the clustered hairs of the fabricated sample pulled the meniscus of water similarly to S. molesta, as shown in Fig. 6. By assuming the shape of the meniscus is elliptical as shown in Supplementary Fig. 7, the minimum interfacial energy W required for the meniscus to form is where A is the interfacial area of the meniscus; a and c are the elliptical fitting parameters; and σ and σ * are the surface tension of the liquid and the interface tension of the contact area, respectively 20 . As the meniscus pulling force is equal to its water adhesion force, it could be calculated as The calculated meniscus pulling force of a single clustered hair was 19.9 μN, comparably similar to that of S. molesta (19.5 μN) 20 . As provided under Supplementary Fig. 7, the meniscus pulling force can also be calculated using different method, which gives values in a similar range [46][47][48] .
Given the meniscus pulling force and number of clustered hairs per unit area, the maximum outward pressure oscillation of the waterair interface the fabricated sample could hold without breaking a pin could be assumed as~217 Pa.
In general, an effective slip length of the surface is used to quantitatively compare the effect of HDR 18 . The effective slip length of the prepared Salvinia-inspired surfaces was measured using a rotational rheometer. Apparent viscosity of 40 wt% glycerol was measured on the sample surface and the reference plate to calculate the effective slip length to quantitatively evaluate the HDR effect of the fabricated sample, as shown in Fig. 7. From Eq. (15), the effective slip length was found to be~137 μm 49 . For a torsional Couette flow, by using the measured apparent viscosities from the rheometer test, the drag reduction on the sample surface could also be calculated as~82.0% from the following equation: A hierarchical micro-pillar array was designed, replicated by soft lithography, and uniformly clustered by inducing capillary force. Afterward, through hydrophobic and hydrophilic coating processes, the heterogeneous wettability of Salvinia was also successfully mimicked. Due to its gently curved structure and local hydrophilicity, the Salvinia-inspired surface exhibited high meniscus pulling force to maintain a stable air-water interface while minimizing the water-solid contact area. By using a rotational rheometer test, a high level of effective slip length was measured on the Salvinia-inspired surface. Given that the hierarchical micropillar template for the CFIC could be prepared by conventional soft lithography processes, which is easy to apply to a continuous fabrication process, it is expected to contribute to the commercialization of HDR surface.

Master mold fabrication
The original master mold with hierarchical pillar arrays was 3D printed by Photonic Professional GT (Nanoscribe GmbH) by using IP-S resin on an ITO coated glass, with 1 μm resolution. After the fabrication, the mold went through a passivation process to ensure defect-less release in the following soft lithography processes.

Soft lithography
Templates for the capillary-force-induced clustering were prepared following a typical soft lithography protocol by using PDMS (Sylgard 184, Dow Corning) with 10:1 base to curing agent ratio. PDMS precursor was poured onto the master mold and cured in 70°C oven for 2 h before demolding to prepare negative type replica mold. The negative type, first-generation PDMS replica mold was baked in 150°C oven for 2 h for defect-less release in the following self-replication. By using the first-generation replica as a mold, the positive type, secondgeneration PDMS replica was replicated following the same typical protocol and then used as a template for CFIC. c Micropillar tips making contact with one another. d Clustered micropillars right after the PVA solution dried off the surface.  Capillary-force-induced clustering PVA solution (0.1 wt%) was prepared by mixing DI water with PVA (Sigma Aldrich) powder. The PVA solution was applied on the patterned area of the as-prepared second-generation PDMS replica. After bubbles were removed, the PDMS template with PVA solution on it was placed in a 70°C convection oven until the solution dried out completely.

Fixing the clustered tips with additional PDMS
The clustered tips were carefully inked by additional PDMS. The inked PDMS was fully cured in a 70°C oven to fix the clustered tips in the position.

Additional hydrophobic and hydrophilic coatings
The entire sample surfaces were coated with commercial hydrophobic wax solution (Ultra ever dry-top coat, UltraTech International, Inc). The was solution was applied to the entire surfaces. After drying, excessive wax was blown off the surfaces by compressed air. To make the clustered pillar tips hydrophilic, the clustered tips were coated by PDA by leaving the tips in contact with the DA solution for 24 h. The DA solution was prepared using dopamine hydrochloride (Sigma Aldrich) and Tris-HCL buffer solution at pH 8.5.

Rheometer test
A rotational rheometer (HAAKE MARS, Thermo Fisher Scientific) was used to measure the apparent viscosity of 40 wt% glycerol using a plate probe with a diameter of 20 mm. The apparent viscosity of the solution was measured on the reference plate and Salvinia-inspired sample surfaces. Multiple Salvinia-inspired surfaces samples were put together to fully cover the probe area. The distance between the measuring surfaces and the probe was controlled to be 30 μm. 10 ml of the solution was applied carefully between the sample surface and the rotating probe by using a syringe.

Data availability
The data that support the findings of this study are available within this paper and or included in the Supplementary Information, and from the corresponding authors upon request. Source data are provided with this paper.